I want to see this yet-unnamed site succeed. There's clearly no lack of technical talent here to make sure the site works, and whether it's popular or not is another question entirely, but what I'm worried most about money.
I don't think it's as important to be a non-profit as it is that its operation is funded directly by the community occasionally opening their wallets. Having a userbase of people who find it valuable and think it's worth paying for is what will keep this site going for a long time. If it starts to suck, or heads in a direction users don't like, the users can choose not to continue supporting it.
Ads suck. CPMs are low, ad networks are basically a backdoor and moderately technical users are going to block ads for one reason or another.
Premium memberships also suck. A lot of people either don't have money or don't have an easy way of spending it online, are 16 years old, live in a country where payments aren't easy, etc. and discouraging contributions or creating two classes of users leads to a less vibrant community.
What's left? Direct donations during a funding drive (annual? semi-annual? as-needed?), paired with visibility of some kind for those who contribute a certain amount during the latest funding drive. A gold star next to your UID, a thumbs-up icon, etc. Something that signifies that this person is a supporter of the site and lets the user feel proud. Of course, for the especially humble or private, you should be able to hide yours.
Perhaps there could also be a cap on the total amount of funding the site can receive in any one funding period. The admins would set an amount they think is adequate, and once the amount is reached, the ability for users to participate in that funding is disabled. This could be useful for visibly combating any tendency towards greed and proving to users that a maximal pile of money is not what they're after. Plus, combined with the 'gold star' idea from the previous paragraph, those who rush to support the site with wallets open get "rewarded" for being quick to contribute money before the cap is reached.
To keep this site running long-term, there needs to be a culture of opening your wallet, putting money where your mouth is, etc., from day one. Voluntarily. I think people who have seen the ad-ridden pageview-chasing modern web know why this is important. If the site is valuable to you, and you can, you should support the site directly.